From Eternity to Book Club: Chapter Six

By Sean Carroll | February 16, 2010 7:29 am

Welcome to this week’s installment of the From Eternity to Here book club. Chapter Six is entitled “Looping Through Time.” It’s about both the logical paradoxes presented by time travel, and some of the obstacles to actually building a time machine (closed timeline curves) in general relativity.


Everyone knows what a time machine looks like: something like a steampunk sled with a red velvet chair, flashing lights, and a giant spinning wheel on the back. For those of a younger generation, a souped-up stainless-steel sports car is an acceptable substitute; our British readers might think of a 1950s style London police box. Details of operation vary from model to model, but when one actually travels in time, the machine ostentatiously dematerializes, presumably to be re-formed many millennia in the past or future.

That’s not how it would really work. And not because time travel is impossible and the whole thing is just silly; whether or not time travel is possible is more of an open question than you might suspect. I’ve emphasized that time is kind of like space. It follows that, if you did stumble across a working time machine in the laboratory of some mad inventor, it would simply look like a “space machine”—an ordinary vehicle of some sort, designed to move you from one place to another. If you want to visualize a time machine, think of launching a rocket ship, not disappearing in a puff of smoke.

There might not be too much new to say about this chapter, as part of it appeared as an excerpt in Discover and we’ve already talked about that. But maybe you weren’t reading that post, in which case, it’s new to you!

There were three main goals in this chapter. The first was to explain what time travel would and would not be, in the context of general relativity — in particular, it would be just another form of travel through spacetime, not involving any disappearing and rematerializing at some other point in the past. The second was to go through some of the possible ways to make closed timelike curves (with wormholes or cosmic strings) and see how difficult it really was.

But the third and most interesting goal was to connect time machines to the arrow of time and entropy. At this point in the book we’ve only introduced these concepts somewhat casually — the careful exploration of entropy is in Part Three, which begins next week — so one could argue that a more logical presentation would have delayed this discussion for later. But sometimes there are considerations beyond logic; in particular, once we built up momentum with the entropy discussion, a digression on time travel would have seemed like wandering too far afield. That was my feeling at the time, anyway.

This is a really interesting aspect of time travel, which I think is dramatically under-emphasized in discussions about it: the real reason why traveling backwards in time makes us nervous is that it becomes impossible to define a consistent arrow of time. The arrow is very ingrained in how we think about the world, including the sense that the past is set in stone while we can still make choices that affect the future. In the presence of a time machine part of our personal “future” is already in the “past,” which seems to compromise our free will.

So be it! Our free will was always an approximation, if we are good materialists who believe in the laws of physics. But it’s a highly useful approximation. It’s always worth emphasizing, when you start talking about the paradoxes of time travel: the simplest and most plausible way out is to imagine that the universe doesn’t (and won’t ever) actually have any time machines.

  • Oded

    This question belongs to the previous chapter, sorry I missed posting it then:

    In the book you talked about GR being time symmetric and offered white holes as the time symmetric counterpart of black holes (if I understood correctly?)

    I fail to see how GR is time symmetric. It says that massive objects always pull the “future” direction of light cones towards them, never the “past” part of the light cone. And, I’m not sure I understand how a black hole is reversible at all… As everybody keeps saying, once it’s in, it’s gone forever.. That explicitly needs the arrow of time.

  • Jesse M.

    In a spacetime with closed timelike curves, is it possible to consistently define the local arrow of time along every worldline so that two worldlines intersecting at a single point will always agree which light cone is the future light cone of that event and which is past light cone? In other words, imagine drawing little arrows at each point along a given wordline which show which direction is considered the future from that point, in such a way that the arrows don’t abruptly flip directions at any point along that worldline (you should be able to do this for a closed timelike curve too, it would be like deciding whether the arrows go ‘clockwise’ or ‘counterclockwise’ around the curve). Then can you assign the arrows for each possible worldline in a consistent way, so that for any point where two worldlines cross, their future arrows both point in the same direction? That way you’d never have two observers pass next to each other and each see the other’s clock running backwards…

  • Sean

    Oded– That’s actually not true. Massive objects “pull” things toward them in both directions of time. Throw a baseball into the air — its trajectory is completely time-symmetric. An individual black hole is not time-symmetric, nor is a white hole; but the combination of both is, and they’re both equally good solutions.

    Jesse– It’s possible to consistently line up “past/future” light cones even in the presence of closed timelike curves. (At least it can be possible; we can also think of counterexamples, but those are even crazier than ordinary closed timelike curves.) So in the kinds of time machines we’re talking about, nobody ever sees anyone else’s clock run backwards.

    But I don’t want to call that an “arrow” of time, for a simple reason: entropy cannot increase everywhere along a circle. We can consistently label one direction “the future,” but entropy can’t consistently go up in that direction, if there is a closed timelike curve.

  • Mike

    Some further background on the possibility for time travel in connection with CTCs:


    At the above link is an equation from a paper by David Deutsch: Quantum Mechanics near Closed Time-like Lines which appeared in Physical Review D44, 3197–3217 (1991).

    According to Deutsch, it is the equation for the state of a quantum computer that is, by whatever means, provided with a method of sending its output back in time to interact with its input. I suppose this is “merely” a question of engineering :)

    He believes that the universality of quantum computation ensures that the results also apply to any time-travelling physical system, not just a quantum computer.

    He says that analysis of the equation shows that if we had a time machine and tried to use it to enact ‘paradoxes’ (like going back in time to prevent our building the time machine), we would simply go back to a universe in which those events really happened.

    Of course, this begs the question whether quantum gravity will ultimately allow for CTCs, and even if it does, whether the “engineering” obstacles can realistically be overcome. In any event, it’s an interesting and thought provoking question.

    Thanks Sean.

  • Sean

    All very true. The discussion of time travel in this chapter was presuming classical general relativity, no quantum mechanics — things are confusing enough as it is.

  • Lawrence Kuklinski

    Hello Sean,
    When I look thru my telescope at the light from distant galaxies I assume I am seeing their past thru the photons they have sent. Does this imply that their past exists in our present? Does that suggest that our past still exists in the light that we have sent out?

  • Lawrence M Kuklinski

    Concerning Mike’s comment:

    Does time travel exist on the Quantum field for “Virtual Particles”?
    Can you borrow something from either the past or the future to use in the present?

  • Mike


    I’m really not well versed enough to respond in any kind of detail. My recollection is that at least as recently as 1998, Deutsch thought, for example, that “borrowing” from another time/universe would not involve (i) “virtual particles” (they would be as real as the particles in our time/universe), nor (ii) the creation, out of nothing, of complex human knowledge. Like other aspects of time travel (which may or may not be achieved one day), trade throughout the “multiverse” would not be paradoxical. But, I’m sure there are many who would disagree :)


  • Lawrence Kuklinski

    What future discoveries are to be made!
    A grand time to be alive.
    Any comment on #7? I have an 18″ Dob telescope that I use for deep sky viewing and I often ponder over the images I see made with photons journeying thru spacetime. I wonder if our past exists in the photons we send out. Could we catch up to them thru an inflationary mechanism per Dr Alan Guth?

  • Sean

    Lawrence– We’ll be talking a bit more about this later in the book. When you observe photons today, you’re not observing the past; you are observing photons today. We can reconstruct certain facts about the past, based on the conditions of those photons — but doing that reliably requires some assumption about a low-entropy past. (A perfectly reasonable assumption which everyone makes all the time.)

  • Lawrence Kuklinski

    You just gave me a reverse epiphany!
    An idea I had for years is not true.
    All these years I assumed that the light from distant galaxies were from the original photons and contained past information. Where in your book is this discussed? Can you suggest any additional references that discuss this concept. I must update my idea of the subject.

    Thank you

  • Sean

    We believe that they are the same photons as were emitted from distant galaxies many years ago. But that is a belief, not something we directly measure. All we measure are photons in our detectors.

  • Lawrence M Kuklinski

    Your discussion of Time would make a great subject for a Teaching Co program.
    Just my thoughts.

  • Joe Polchinski

    Hi Sean,

    I started your book recently and am enjoying it. You present some standard material in a fresh way, as well as topics not so often covered. However, I think that chapter 6 is out of place. It distracts from the otherwise tightly reasoned argument: the reader does not need to be confronted with hypothetical questions about free will, which depend in turn on limited results about mathematical physics without Cauchy surfaces (in contrast to most everything else in the early chapters, which is well-vetted in the scientific literature).

  • Jesse M.

    Hi Sean, in response to my question about local arrows of time in spacetimes with CTCs you said:
    But I don’t want to call that an “arrow” of time, for a simple reason: entropy cannot increase everywhere along a circle. We can consistently label one direction “the future,” but entropy can’t consistently go up in that direction, if there is a closed timelike curve.

    But isn’t the relation between entropy and the arrow of time more complicated when we’re talking about a non-isolated system? A macroscopic object following a closed timelike curve might have its entropy lowered by an interaction with the external environment on some segment of its worldline (so that its entropy could self-consistently be increasing over the rest of its worldline), that doesn’t seem equivalent to saying the arrow of time was actually going backwards in a small region of spacetime containing that segment (or a portion of that segment).

  • Sean

    Jesse– Yes, it certainly is more complicated for individual subsystems that may travel around closed timelike curves. But we also want there to be (or at least are used to there being) a consistent arrow of time for the whole universe, which is hard to define in the presence of CTC’s.

    Joe– You might be right. Kip Thorne had similar concerns, so if you both have that reaction I must be doing something wrong. But I suspect it’s a communication failure on my part, rather than a problem with the topic. I did talk about the problem of determining what would happen in the future if there were closed timelike curves, which reduces to the issue with Cauchy surfaces, but that’s definitely not the major point I’m trying to get across. Which is: we are bugged at a visceral level by time travel, and the reason why is because we lose the clean division between “past” (already happened, set in stone) and “future” (yet to occur, and therefore something we can still hope to influence through our choices). And the reason why we ordinarily can rely on that distinction, of course, is because of entropy and the arrow of time.

    So I think it’s a useful illustration of one of the main themes of the book. (Also, if you’re going to write a book about time, people are going to have questions about time travel.) But I’m happy to admit that it might have been better placed somewhere else in the book, or that I let the discussion of determinism cloud up the main thrust of the chapter.

    In any event, Chapter Seven is where the important stuff really starts.

  • Bee

    Hi Sean:

    Can you have CTC’s then between regions of spacetime that have the same entropy? Could you argue the other way round that them having CTC’s implies they have the same entropy?

    I totally disagree with Joe, the part about free will entirely belongs there. If you think readers will ask a question while reading what you wrote, better address that question. Btw, do you believe we really have a free will? Best,


  • Anu

    Hi Sean

    This is a really interesting discussion. I stumbled upon this discussion today and am totally totally enthralled- the time mystery and the questions around time and space have always been questions for me, unanswered – and they beauty lies in them being mysteries i guess. In hope of some answer somewhere, can’t stop to wonder at the inexplicability of our presence in this space, and hence the related question of time – the dimension which we can notice . Have ordered my copy of your book just right now. Hope to get it soon – keenly looking forward.

    Meanwhile, there is a pet idea that I hold regarding time travel. Its less on interference, and more on observation. Rather amateur (if you may). The idea being – If and when it is possible to travel faster than light (say thrice the speed of light) – then why don’t we/ our machines go on some other planet with that speed – and then camp there and observe earth – the photons/view that they observe will represent the past. They can thus see what happened in the past (without interfering with it) – the farther they go and the faster they go, the more of the past (in terms of the common understanding of time’s direction) they can observe. Derived from the fact that when we look at the sun, we look at sun as it was 8 mins back. When we look at something which is say 3 light years away – we reach there in 1 and then try to see what earth looked like…then it would be three years back, for us 2 years back.

    Well, this again assumed a lot of things – levels of entropy being one, and then that its sort of a straight line…i hope i am not intruding into this really technical discussion with this amateur idea, but I really look forward to see some dash of clarity on this huge grey misty inexplicable horizon of universe that we have. Happy even if the idea gets nullified.

    On another note, thanks for this forum…really glad to hear so many people talk about the questions that many others in this world don’t even stop to ponder about.

  • Bee

    Anu: The scenario you outline is not itself problematic. But it becomes problematic if you assume that not only you’d be able to do that sort of trick but everybody. Then it’s Special Relativity spitting in your soup because if you can travel faster than the speed of light what is “future” and what is “past” become ambiguous, and you end up being able to send messages to yourself in the past. Best,

  • Anu

    Thanks Bee.

    My idea was more around observation…assuming that not me or someone else but may be some bots/machines/ willing people overtake the speed of light to observe it from a point ahead on its straight/curved path. I don’t know what happens if we try to signal back…but if one observes without interfering, wouldn’t one (the bot/ machine) end up ‘seeing’ some fragment of the past….and then once it has recorded it, bring it back for us to observe and analyse?

    It may not be fun if it is just one or two years kind of distance…but if it is possible for one year, then it can be for 50 yrs or 100 yrs …can it then record what happened in 1910 and bring it back for us to observe….though the people who observe it may not be us, but those of a few generations later.

    All this assumes that we are just observing. The signalling/interfering may happen if you reflect back at the same speed as you travel (that is faster than light). So the underlying assumption is that one travels a few times faster than light. Actually, even a second faster would make it theoretically possible.

    On a lighter note, I really won’t mind a ‘Hi” from a future-me to the past-me :)

  • Sean

    Bee– Having a CTC connect two regions of space isn’t all that different from having an ordinary timelike curve connect them — it just that they’re connected both ways. So you can certainly have the same entropy along the CTC, if you have a system in equilibrium. But it doesn’t have to stay constant, it just has to come back to where it started. Because there’s no reason to assume that the system is closed, there’s nothing to stop the entropy from increasing and then decreasing again, although it might require some ridiculous fine-tuning.

    I don’t believe in a strong Kantian type of free will, in which agents are laws unto themselves over and above the laws of nature. But I do believe in an effective kind of free will that simply results from our inability to accurately predict the future on the basis of incomplete information. That’s what becomes problematic in the presence of time travel.

    Anu– As Bee says, there is a well-known fact in special relativity, that if you can (reliably and controlably) travel faster than the speed of light, then you can travel backwards in time. You could imagine more complicated theories in which there was still an upper speed limit, which just wasn’t equal to the speed of light, and which prevented time travel.

  • Bee

    Hi Sean,

    Thanks. I’m not sure what you mean with “effective” here. I of course agree that we’re not able to predict the future. The actual question is whether you think you can change it, or whether you think you just think you can change it. It boils down to whether or not you believe time-evolution to be entirely deterministic or not. By the chapter I’m currently reading you haven’t yet said “quantum,” so I’m curious. Best,


  • Susan

    I got the audiobook and yes the reader is good. He is very clear.and he avoids sounding like he is reading the Old Teste ment. He does, however, have the same timing and tone as Spock in the latest movie. That isn’t a bad thing. While I liked your voice just fine in your lectures, and I like consistency, I guess Erik Synnestvedt (sounds Vulcan) is a good choice. 16.5 hours of listening is a good buy. I am enjoying the book, both styles.

  • William Barham

    Finished your book today. Will begin to re-read it soon… left some questions along the way. You book and, many others, have stimulated this recurrent question. I am sure it will impact you as one of the dumbest and most illogical questions you have ever been asked. The question being: When a wave function collaspes, is any mass created; no matter (no pun) how infinitesimally small ?
    Apology for my ignorant condition

  • Lab Lemming

    Can you provide backlinks to previous chapters in this series for those of us whose international copies just came in?

  • Sean
  • Corey

    I thought that the Gate into Yesterday was an interesting thought experiment. Using a human to illustrate the point of course makes the scenario highly unlikely, especially as you indicated that every atom in his body needs to line up and every speck of dust needs to be the same on either side of the gate.

    However, I think that the scenario becomes less far-fetched when you consider individual particles, which travel as waves unless measured. Since we are uncertain about the exact position of a particle at any given moment, we are unable to determine whether it crosses through the gate in the same exact position each time. Also, we are uncertain about the precise time that the particle crosses through the gate. In fact, at some point on the particle’s world line, the probability distribution of its location in spacetime would span both sides of the gate. Does that concept conflict with any known laws of physics or would that be permitted?

    Also, closed timelike curves can exist without containing particles, thus also eliminating the issues that you discussed.

    Just for fun, could we have an example that is even more odd than your scenario? Could the stranger that you describe, whose life story you described as “a one-day loop repeated ad infinitum,” actually walk through the gate facing forwards on one day, then walk through the gate facing backwards the next day (in his world line), then restart the loop by walking through forwards again such that he lines up exactly with his past self? In this way, we create a two-day loop, occurring within a single day, perhaps playing out in two parallel universes. I understand only a little about how “spin” works in quantum physics, but isn’t this the concept of how some particles must rotate twice to return to their original position?

    Regardless, if closed timelike curves were to exist, we can be certain that the conditions would not permit the evolution of conscious beings, so paradoxes in terms of free will not occur.

  • Stevie

    Uh, Sean, couldn’t you have come up with a more original title and cover art for the book - ? That one is from March 2009…

  • Sean

    Corey– I don’t think that switching from particles to waves makes any difference. Waves have definite values at every event, just like particles; you shouldn’t think of waves as “particles whose positions we don’t precisely know.” But your complicated example is perfectly reasonable (at least within the confines of this thought experiment).

    Stevie– Unfortunately not; by the time we knew about Viola’s book, the die had been cast, as it were.

  • Bee

    I’m disappointed, you haven’t answered my question: Do you think we can change the future by your actions, or do you think we just have the impression we can change it? Saying you believe in an “effective” kind of free will from our inability to predict the future seems to mean to me you do not believe you can change the future (as in: it’s entirely determined), which I would argue means simply you don’t believe in free will. Best,


    PS: A comment subscription feature for the posts here would be handy. I tend to forget about comments I’ve made if I don’t get replies by email.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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